The issue is not whether the baby ‘gets’ its blood from the mother. The question was whether the blood mixes. It does.
John 6:63 "The flesh profits nothing"
The assertion was that Christ got ALL of His blood from His mother.
IF it mixes at all, it is only a temporary situation. If you and your best buddies decided to be "blood brothers" by cutting yourselves and touching those cut areas to each other to do so, your blood doesn't change, does it? Sure, it might be a good way to get a blood-born infection, but it is not a way to actually BE carrying each other's blood.
The reason this was brought up was in reply to another's assertion that Jesus got his blood from Mary. But human babies have their OWN unique blood separate from both the mother's and father's blood. Besides....isn't there a semi-dogmatic idea Catholics have that says Mary didn't suffer in her childbirth, that her hymen was not broken? If so, then there wouldn't BE even any blood mixing going on between Jesus and Mary.